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A092509 Möbius transform of sequence A008475. 2
0, 2, 3, 2, 5, 0, 7, 4, 6, 0, 11, 0, 13, 0, 0, 8, 17, 0, 19, 0, 0, 0, 23, 0, 20, 0, 18, 0, 29, 0, 31, 16, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 43, 0, 0, 0, 47, 0, 42, 0, 0, 0, 53, 0, 0, 0, 0, 0, 59, 0, 61, 0, 0, 32, 0, 0, 67, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 54, 0, 83, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

a(n) = 0 if n is 1 or not a power of a prime;

a(n) = n if n is a prime;

a(n) = n*(1 -1/p) if n = p^k, k>= 2, p=prime.

a(n) = Sum_{d|n} A008683(d)*A008475(n/d). - Antti Karttunen, Nov 17 2017

MATHEMATICA

f[n_] := Plus @@ Map[Power @@ #1 &, FactorInteger[n]]; mt[n_] := Block[{d = Divisors[n]}, Plus @@ (MoebiusMu /@ (n/d)*f /@ d)]; Table[ mt[n], {n, 93}] (* Robert G. Wilson v, Jan 12 2005 *)

PROG

(PARI)

A008475(n) = { my(f=factor(n)); vecsum(vector(#f~, i, f[i, 1]^f[i, 2])); };

A092509(n) = sumdiv(n, d, moebius(d)*A008475(n/d)); \\ Antti Karttunen, Nov 17 2017

CROSSREFS

Cf. A008475, A008683.

Sequence in context: A059051 A130069 A120007 * A214053 A214056 A014973

Adjacent sequences:  A092506 A092507 A092508 * A092510 A092511 A092512

KEYWORD

nonn

AUTHOR

Leroy Quet, Dec 31 2004

EXTENSIONS

More terms from Robert G. Wilson v, Jan 13 2005

STATUS

approved

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Last modified March 30 15:42 EDT 2020. Contains 333127 sequences. (Running on oeis4.)